Operating line equation

Equation 32 represents the upper (or rectifying) operating line equation and equation 33 represents the lower (or stripping) operating line equation. The slopes L jV and L jV can vary, depending on heat effects. 

The McCabe-Thiele method employs the simplifying assumption that the molal overflows in the stripping and the rectification sections are constant. This assumption reduces the rectifying and stripping operating line equations to ... 

The slope L/V of the operating line is termea the internal-reflux ratio. This ratio in the operating-line equation for the top section of the column [see Eq. (13-21)] is related to the external-reflux ratio R = L + i/D by... 

Note This is not too accurate due to switched operating line equations before the feed compositions were reached, yet, one more calculation on the stripping line would have placed us below the feed plate composition. Hence a change in reflux ratio is necessary in order to split right at the feed composition. 

Using Figure 8-33 the separation from Xq, initial kettle volatile material to X3 as the distillate of more volatile overhead requires three theoretical plates/stages at total reflux. Using finite reflux R4, and four theoretical plates the same separation can be achieved with infinite theoretical plates and the minimum reflux ratio, Rmin- The values of reflux ratio, R, can be determined from the graph with the operating line equation as,... 

AP = pressure drop, in. liquid X, = slope ratio, slope equilibrium line/slope operating line. Equation 8-329 p = density, Ib/ft ... 

For any plate n, neglecting the plate dynamics, the compositions of the passing liquid and vapour streams are represented by the standard operating line equation, where... 

On/off control 96 Operating line equation 595 Optimisation 108 Order of reaction 53, 323 Oscillating tank reactor 350 Oscillations 507, 518, 663... 

Vapour y, leaving the top tray has a composition, xd = 0.95 so that xt, the liquid composition on the top tray, is found from the equilibrium curve to be equal to 0.88. v, i is found from the operating line equation as ... 

The solution may be set out as a table as follows, using the operating line equations and... 

This last value of composition is sufficiently near to that of the feed for the feed to be introduced on plate (f — 3). For the lower part of the column, the operating line equation (ii) will be used. 

Figure 13.7. Features of McCabe-Thiele diagrams for constant molal overflow, (a) Operating line equations and construction and minimum reflux construction, (b) Orientations of -lines, with slope = ql q — 1), for various thermal conditions of the feed, (c) Minimum trays, total reflux, (d) Operating trays and reflux, (e) Minimum reflux determined by point of contact nearest xD.

Slopes of component balance (operating) lines. Equations (2.9) and (2.10) indicate that the slopes of the component balance lines are h V and LTV for the rectifying and stripping sections, respectively. As L < V [Eq. (2.11)] and L > V [Eq. (2.12)], the slope of the rectifying section component balance line is smaller than unify, while that of the stripping section component balance line Is greater than unify. 

By introducing the term for the seed mass, Equation 2 can be modified into an operating line equation for the batch crystallizer ... 

The operating line (Equation 3) can be solved simultaneously with the equilibrium line (Equation 4) to obtain the temperature-time profile for the batch crystallizer. 

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